A ship leaves port on a bearing of 420 and travels 126mi The

A ship leaves port on a bearing of 42.0° and travels 12.6mi. The ship then turns due east and travels 4.7mi. How far is the ship from port, and what is its bearing from port?

Solution

x - component = 4.7 + 12.6sin42 = 13.131 mile

y-component = 12.6cos42 = 9.3636 mile

total distance from port= sqrt(13.131² + 9.3636²) = 16.13 mile

bearing = tan^-1(13.131/9.3636) = 54.5°